{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:14:48Z","timestamp":1777644888565,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2013,5]]},"abstract":"<jats:p>A filtration of a formal language L by a sequence s maps L to the set of words formed by taking the letters of words of L indexed only by s. We consider the languages resulting from filtering by all arithmetic progressions. If L is regular, it is easy to see that only finitely many distinct languages result; we give bounds on the number of distinct languages in terms of the state complexity of L. By contrast, there exist CFL's that give infinitely many distinct languages as a result. We use our technique to show that two related operations, including diag (which extracts the diagonal of words of square length arranged in a square array), preserve regularity but do not preserve context-freeness.<\/jats:p>","DOI":"10.3233\/fi-2013-804","type":"journal-article","created":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T00:20:59Z","timestamp":1575332459000},"page":"135-142","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Filtrations of Formal Languages by Arithmetic Progressions"],"prefix":"10.1177","volume":"123","author":[{"given":"Hamoon","family":"Mousavi","sequence":"first","affiliation":[{"name":"School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada. hamoon.mousavihaji@uwaterloo.ca; shallit@cs.uwaterloo.ca"}]},{"given":"Jeffrey","family":"Shallit","sequence":"additional","affiliation":[{"name":"School of Computer Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada. hamoon.mousavihaji@uwaterloo.ca; shallit@cs.uwaterloo.ca"}]}],"member":"179","published-online":{"date-parts":[[2013,1,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2013-804","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2013-804","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:30:28Z","timestamp":1777444228000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2013-804"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,1]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013,5]]}},"alternative-id":["10.3233\/FI-2013-804"],"URL":"https:\/\/doi.org\/10.3233\/fi-2013-804","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1,1]]}}}